To achieve high accuracy with less computational time in the phase shifting interferometry, a series of two-step random phase shifting algorithms based on fast least-squares method are proposed. First, the phases extracted by the sum and difference normalization algorithm with double pre-filtering, the sum and difference normalization algorithm with single pre-filtering, and Gram-Schmidt orthonormalization method are used as the initial values for iteration. Then, the two phase shifted interferograms without filtering are used in the calculation with the least-squares method, and the final phase is obtained. In order to save time, only limited pixels are chosen to take part in the iteration. The comparison indicates that the two-step phase shifting algorithm based on the sum and difference normalization algorithm with single pre-filtering and fast least-squares method has the best comprehensive performance, and it can obtain high accuracy with less time.